Вправи: 542

542. Спростіть вираз:

1) (a\a+1 – aa+ 1) : aa-1 = (a)2+ a- aa+ 1 : aa-1 = a+ a- a • (a-1)a+ 1 • a = a • a- 1(a+ 1)a+ 1 • a = a – 1;

2) (a+ bb + ba- b) : ab = a+ ba- b+ (b)2b(a- b) : ab = a-b+b • bba- b • a = a(a- b)a = (a)2(a- b)a = aa- b;

3) (x- 3x+ 3 + 12xx-9) : x+ 3x-3x = x.

1. x- 3\x-3x+ 3 + 12xx- 3(x+ 3) = (x- 3)2+ 12xx- 3(x+ 3) = x-6x+ 9+12xx- 3(x+ 3) = x+6x+ 9x- 3(x+ 3) = (x+ 3)2x- 3(x+ 3) = x+ 3x- 3;

2. x+ 3x- 3 : x+ 3x-3x = x+ 3 • x(x- 3)x- 3(x+ 3) = x.

4) a-64a+ 3 • 1a+8a – a+ 8a-3a = a-64 • 1a+ 3 • a(a+ 8) – a+ 8a(a- 3) = a- 8(a+ 8)a+ 3 • a(a+ 8) – a+ 8a(a- 3) = a- 8a(a+ 3) – a+ 8a(a- 3) = a- 8a- 3- (a+ 8)(a+ 3)aa+ 3(a-3a) = a-3a- 8a+ 24-a-8a- 3a- 24aa+ 3(a- 3) = -22aaa+ 3(a- 3) = -22a(a)2- 32 = -22a-9 = 229 -a.